Can currency competition affect central banks' control of interest rates and prices? Yes, it can. In a two-currency world, the growth rate of the cryptocurrency sets an upper bound on the nominal interest rate and the attainable inflation rate, if the government currency is to retain its role as medium of exchange. In a world of multiple competing currencies issued by profit-maximizing agents, the nominal interest rate and inflation are both determined by structural factors, and thus not subject to manipulation, a result hailed by the proponents of currency competition. The article also proposes some fixes for the classical problem of indeterminacy of exchange rates.Can currency competition affect central banks' control of interest rates and prices? Yes, it can. In a two-currency world, the growth rate of the cryptocurrency sets an upper bound on the nominal interest rate and the attainable inflation rate, if the government currency is to retain its role as medium of exchange. In a world of multiple competing currencies issued by profit-maximizing agents, the nominal interest rate and inflation are both determined by structural factors, and thus not subject to manipulation, a result hailed by the proponents of currency competition. The article also proposes some fixes for the classical problem of indeterminacy of exchange rates.